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The problem asks to evaluate the limit \(\lim_{x \to 3} f(x)\) based on the provided graph of the function \(f(x)\).

### Step-by-step analysis:
1. **Behavior near \(x = 3\)**: We observe that as \(x\) approaches 3 from the left and right, the function \(f(x)\) appears to approach a value, but there is a dot at \(y = -3\) indicating a hole or discontinuity.

2. **Left-hand and right-hand limits**:
   - As \(x \to 3^{-}\) (from the left), the function values seem to get closer to \(y = -3\).
   - As \(x \to 3^{+}\) (from the right), the function also appears to approach \(y = -3\).
   
3. **Discontinuity**: The point \( (3, -3) \) is shown as a solid dot, meaning the function might be discontinuous at \(x = 3\). However, this does not affect the limit; we only care about the behavior as \(x\) approaches 3, not the actual value of \(f(3)\).

### Conclusion:
Both the left-hand and right-hand limits approach \(y = -3\), so the overall limit is \(-3\).

### Final Answer:
\[
\lim_{x \to 3} f(x) = -3
\]
The correct choice is **-3**.

Would you like any additional details or have any further questions?

Here are five related questions you can explore:
1. What is the significance of the solid dot at \(x = 3\)?
2. How do left-hand and right-hand limits affect the existence of a limit?
3. What is the difference between a limit and the function value at a point?
4. What types of discontinuities can occur, and how do they impact limits?
5. How do you handle limits at infinity based on graphical behavior?

**Tip**: When evaluating limits graphically, always check both sides (left and right) to confirm whether they approach the same value.

Given the graph of f(x) shown above, evaluate lim (x -> 3) f(x).

This problem involves evaluating the limit lim (x -> 3) f(x) using graphical analysis. Explore how left-hand and right-hand limits converge at x = 3 and determine the impact of discontinuities. Suitable for students in Grades 10-12.

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